A deterministic synchronous shaping and machining method based on two-dimensional surface height error

Abstract

This invention discloses a deterministic synchronous shaping method for optical components based on two-dimensional surface height errors. The method includes converting a height error matrix into a meridional slope error matrix and a sagittal slope error matrix; converting a height removal function matrix into a meridional slope removal function matrix and a sagittal slope removal function matrix; substituting these into a dwell time calculation model for the multidimensional errors of the optical component to be processed and calculating the dwell time matrix; arranging the dwell time matrix according to the two-dimensional surface shape of the optical component to form a two-dimensional dwell time; and using the two-dimensional dwell time to perform deterministic shaping of the multidimensional errors of the optical component to be processed. This invention combines the multidimensional errors of the optical component to calculate the dwell time, enabling simultaneous correction of height and two-dimensional slope errors, which is beneficial for improving the determinism of the processing and the correction effect of multidimensional errors.

Description

Technical Field

[0001] This invention belongs to the field of optical component processing technology, specifically relating to a deterministic synchronous shaping processing method based on two-dimensional surface height error. Background Technology

[0002] Traditional optical component fabrication only imposes strict requirements on height error. However, with the development of X-ray optics, extremely high requirements are now placed on both the height error and two-dimensional slope error of X-ray mirrors. Long-range profilometers can directly measure the one-dimensional slope error information of optical components. However, for deterministic shaping of optical components, a two-dimensional full-aperture surface shape is required. Therefore, two-dimensional height error information obtained from wavefront interferometry is more suitable for deterministic shaping. Current ion beam fabrication models for optical components include height error shaping based on two-dimensional height error and slope error shaping based on one-dimensional slope information. When using height error shaping methods, larger amplitude error components are preferentially corrected, resulting in many high-frequency residual errors and low slope error convergence. When using slope error shaping methods, higher frequency error components are preferentially corrected, leaving low-frequency errors uncorrected, resulting in low height error convergence. In summary, neither the existing deterministic shaping and machining methods based on surface height error nor the deterministic shaping and machining methods based on surface slope error are suitable for machining optical components that require both height error and two-dimensional slope error. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a deterministic synchronous shaping and processing method based on two-dimensional surface height error, which addresses the above-mentioned problems in the prior art. This invention combines the multidimensional errors of optical elements to calculate the dwell time, and can realize the synchronous correction of multidimensional errors (height error and two-dimensional slope error), which is beneficial to improve the determinism of the processing process and improve the correction effect of multidimensional errors.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0005] A deterministic synchronous shaping and machining method based on two-dimensional surface height error includes:

[0006] S101, Obtain the height error matrix of the optical element to be processed. and height removal function matrix ;

[0007] S102, the height error matrix Convert to meridian slope error matrix and the slope error matrix of the arc direction The height removal function matrix Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix Substitute the following formula into the residence time calculation model for the multidimensional error of the optical element to be processed:

[0008] ,

[0009] In the above formula, The weight value representing the height error. The weighted value representing the slope error along the meridian direction. This represents the weighting value for the slope error in the sagittal direction. Represents the residence time matrix;

[0010] S103, The residence time matrix is ​​calculated based on the residence time calculation model of multidimensional error. , residence time matrix Arranged according to the two-dimensional surface shape of optical elements to form a two-dimensional residence time And utilize two-dimensional dwell time Deterministic correction of multidimensional errors in optical components to be processed.

[0011] Optionally, in step S102, the height error matrix is... Convert to meridian slope error matrix and the slope error matrix of the arc direction This refers to the height error matrix The meridian slope error matrix is ​​obtained by performing difference operations at adjacent error points in the X and Y directions respectively. and the slope error matrix of the arc direction .

[0012] Optionally, in step S102, the height removal function matrix is... Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix This refers to removing the height function matrix. The meridian slope removal function matrix is ​​obtained by performing difference operations on adjacent data points in the X and Y directions respectively. and the slope of the arc direction removal function matrix .

[0013] Optionally, before step S102, a residence time calculation model for the multidimensional error of the optical element to be processed is also included:

[0014] S201, construct the convolution relationship equation between surface error, dwell time, and removal function as shown in the following equation:

[0015] ,

[0016] In the above formula, The two-dimensional height surface shape of the optical element to be processed. For height removal function, This represents the convolution operation. Indicates the two-dimensional dwell time;

[0017] S202, convert the convolution relationship equation into a system of linear equations:

[0018] ,

[0019] In the above formula, Represents the height error matrix. This indicates the removal of the function matrix. Represents the residence time matrix;

[0020] S203, Based on the aforementioned linear equations, establish a deterministic linear model for shaping and machining of the meridional slope error and the sagittal slope error:

[0021] ,

[0022] ,

[0023] In the above formula, This is the slope error matrix along the meridian direction. The slope error matrix is ​​the arc direction. The function matrix is ​​removed to represent the slope in the meridional direction. Remove the function matrix from the slope of the arc direction;

[0024] S204 combines the linear equation system, the meridional slope error, and the sagittal slope error of the deterministic shaping linear model to obtain the dwell time solution model for the multidimensional error of the optical element to be processed.

[0025] Optionally, in step S103, the residence time matrix is ​​calculated using the residence time calculation model based on multidimensional error. This refers to a residence time calculation model based on multidimensional error, which uses the LSQR algorithm to calculate the residence time matrix. .

[0026] Optionally, before step S102, the method further includes obtaining the weight values ​​of the height error configured by the user. Weighting value of meridian slope error and the weighting value of the slope error in the sagittal direction .

[0027] Optionally, step S103 utilizes two-dimensional dwell time. After performing deterministic shaping of the multidimensional errors of the optical element to be processed, the process also includes measuring the height error RMS, meridional slope error RMS, and sagittal slope error RMS of the processed optical element.

[0028] Furthermore, the present invention also provides a deterministic synchronous shaping machining system based on two-dimensional surface height error, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the deterministic synchronous shaping machining method based on two-dimensional surface height error.

[0029] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program / instructions that are programmed or configured to execute the deterministic synchronous shaping and machining method based on two-dimensional surface height error by a processor.

[0030] In addition, the present invention also provides a computer program product, including a computer program / instruction, which is programmed or configured to execute the deterministic synchronous shaping and machining method based on two-dimensional surface height error by a processor.

[0031] Compared with the prior art, the present invention has the following main advantages: The present invention includes the use of a height error matrix. Convert to meridional slope error matrix and sagittal slope error matrix, then remove the height function matrix. The process involves converting the slope removal function matrix in the meridional direction and the slope removal function matrix in the sagittal direction. These are then substituted into the dwell time calculation model for the multidimensional errors of the optical element to be processed, and the dwell time matrix is ​​calculated. This dwell time matrix is ​​then arranged into a two-dimensional dwell time according to the two-dimensional surface shape of the optical element. The two-dimensional dwell time is then used to perform deterministic shaping of the multidimensional errors of the optical element to be processed. This invention combines the multidimensional errors of the optical element to calculate the dwell time, enabling simultaneous correction of height errors and two-dimensional slope errors. This improves the determinism of the processing and enhances the correction effect of multidimensional errors. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0033] Figure 2 The two-dimensional height error surface shape of the optical element to be processed in this embodiment of the invention. .

[0034] Figure 3 The two-dimensional meridional slope error surface shape of the optical element to be processed in this embodiment of the invention. .

[0035] Figure 4 The two-dimensional arc sagittal direction slope error surface shape of the optical element to be processed in this embodiment of the invention. .

[0036] Figure 5 The height removal function used in the embodiments of the present invention .

[0037] Figure 6 This is the two-dimensional height error surface shape of the optical element after processing in an embodiment of the present invention.

[0038] Figure 7 This is the two-dimensional meridional slope error surface shape of the optical element after processing in this embodiment of the invention.

[0039] Figure 8 This is the two-dimensional arc-slope slope error surface shape of the optical element after processing in this embodiment of the invention. Detailed Implementation

[0040] In this example, the optical element to be processed is a single-crystal silicon planar mirror with an effective area of ​​15mm × 270mm. The following will take this optical element to be processed as an example to further explain the multi-dimensional error deterministic shaping and processing method based on the two-dimensional height error of the surface shape of the present invention.

[0041] like Figure 1 As shown, the deterministic synchronous shaping and machining method based on two-dimensional surface height error in this embodiment includes:

[0042] S101, Obtain the height error matrix of the optical element to be processed. and height removal function matrix ;

[0043] S102, the height error matrix Convert to meridian slope error matrix and the slope error matrix of the arc direction The height removal function matrix Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix Substitute the following formula into the residence time calculation model for the multidimensional error of the optical element to be processed:

[0044] ,

[0045] In the above formula, The weight value representing the height error. The weighted value representing the slope error along the meridian direction. This represents the weighting value for the slope error in the sagittal direction. This represents the dwell time matrix; in this embodiment, the multidimensional error includes three dimensions of error: altitude error, meridian slope error, and sagittal slope error.

[0046] S103, The residence time matrix is ​​calculated based on the residence time calculation model of multidimensional error. , residence time matrix Arranged according to the two-dimensional surface shape of optical elements to form a two-dimensional residence time And utilize two-dimensional dwell time Deterministic correction of multidimensional errors in optical components to be processed.

[0047] In step S102 of this embodiment, the height error matrix is... Convert to meridian slope error matrix and the slope error matrix of the arc direction This refers to the height error matrix The meridian slope error matrix is ​​obtained by performing difference operations at adjacent error points in the X and Y directions respectively. and the slope error matrix of the arc direction In step S102 of this embodiment, the height removal function matrix is... Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix This refers to removing the height function matrix. The meridian slope removal function matrix is ​​obtained by performing difference operations on adjacent data points in the X and Y directions respectively. and the slope of the arc direction removal function matrix Specifically, in this embodiment, the elevation error matrix is ​​differentially calculated in the Y direction at intervals of one data point to obtain the slope error matrix in the sagittal direction. The meridional slope error matrix is ​​obtained by subtracting the height error matrix every 30 data points (the length of the optical element in the Y direction) in the Y direction. Similarly, the elevation removal function matrix is ​​subtracted along the Y-axis at intervals of one data point to obtain the slope removal function matrix in the sagittal direction. The height removal function matrix is ​​subtracted in the Y direction at 30 data points intervals to obtain the meridional slope removal function matrix. .

[0048] Before step S102 in this embodiment, a residence time calculation model for the multidimensional error of the optical element to be processed is also included:

[0049] S201, construct the convolution relationship equation between surface error, dwell time, and removal function as shown in the following equation:

[0050] ,

[0051] In the above formula, The two-dimensional height surface shape of the optical element to be processed. For height removal function, This represents the convolution operation. Indicates the two-dimensional dwell time;

[0052] S202, convert the convolution relationship equation into a system of linear equations:

[0053] ,

[0054] In the above formula, Represents the height error matrix. This indicates the removal of the function matrix. Represents the residence time matrix;

[0055] S203, Based on the aforementioned linear equations, establish a deterministic linear model for shaping and machining of the meridional slope error and the sagittal slope error:

[0056] ,

[0057] ,

[0058] In the above formula, This is the slope error matrix along the meridian direction. The slope error matrix is ​​the arc direction. The function matrix is ​​removed to represent the slope in the meridional direction. Remove the function matrix from the slope of the arc direction;

[0059] S204 combines the linear equation system, the meridional slope error, and the sagittal slope error of the deterministic shaping linear model to obtain the dwell time solution model for the multidimensional error of the optical element to be processed.

[0060] In step S103 of this embodiment, the residence time matrix is ​​calculated using a residence time calculation model based on multidimensional error. This refers to a residence time calculation model based on multidimensional error, which uses the LSQR algorithm to calculate the residence time matrix. It should be noted that the LSQR algorithm is a well-known existing method, as detailed in the following literature: Michael A. Saunders, "Solution of sparse rectangular systems using LSQR and Craig's method," BIT Numer. Math., vol.35, no. 4, pp. 588-604, Dec. 1995, doi: 10.1007 / bf01739829.

[0061] Before step S102 in this embodiment, the weight values ​​of the height error configured by the user are obtained respectively. Weighting value of meridian slope error and the weighting value of the slope error in the sagittal direction .

[0062] In step S103 of this embodiment, a two-dimensional dwell time is utilized. After performing deterministic shaping of the multidimensional errors of the optical element to be processed, the process also includes measuring the height error RMS, meridional slope error RMS, and sagittal slope error RMS of the processed optical element.

[0063] In this embodiment, the two-dimensional height error within the effective aperture of the optical element to be processed is obtained by interferometry, as shown below. Figure 2 As shown, differentiating along the X direction yields the meridian slope error as follows: Figure 3 As shown, differentiating along the Y direction yields the meridian slope error as follows: Figure 4 As shown. Height error The root mean square (RMS) value is 10.063 nm, the RMS of the meridional slope error is 0.57 μrad, and the RMS of the sagittal slope error is 0.55 μrad. The two-dimensional removal function obtained in this embodiment... like Figure 5 As shown, its beam diameter is 10mm. The two-dimensional height error... The height data points are discretized into 16200 points at 0.5mm intervals and arranged along the Y direction to form a height error matrix with a dimension of 16200×1. Similarly, the removal function is discretized into 400 points at 0.5mm intervals, and the height data points of the removal function at a certain point are... The amount of material removed from the entire optical element per unit dwell time is a material removal vector. The material removal vectors at all data points can be combined into a removal function matrix. Finally, in this embodiment, the residence time matrix is ​​solved using the LSQR algorithm. The dwell time is determined by arranging the two-dimensional surface of the optical element into a 30×540 dimension. A deterministic reshaping process based on dwell time control is performed. In this embodiment, the processing and inspection results of the optical element after deterministic reshaping are as follows: Figure 6 , Figure 7 and Figure 8 As shown, the height error RMS of the processed optical element converges to 0.961 nm, the meridional slope error RMS converges to 0.19 μrad, and the sagittal slope error RMS converges to 0.29 μrad.

[0064] In summary, this embodiment, based on the deterministic synchronous shaping and machining method of two-dimensional surface height error, establishes the slope error and slope removal function in the meridional direction and the slope error and slope removal function in the sagittal direction according to the two-dimensional height error and two-dimensional height removal function of the optical part to be processed. Furthermore, it establishes multi-dimensional surface error and multi-dimensional removal function through a system of linear equations. In the dwell time calculation, different weight values ​​are set according to the machining requirements of different errors, specifically improving the machining effect of key errors. This avoids the problem of convergence of only a single error in height machining mode and slope machining mode, greatly improving the machining accuracy of multi-dimensional errors and the determinism of the machining process.

[0065] Furthermore, this embodiment also provides a deterministic synchronous shaping machining system based on two-dimensional surface height error, including a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the deterministic synchronous shaping machining method based on two-dimensional surface height error.

[0066] Furthermore, this embodiment also provides a computer-readable storage medium storing a computer program / instructions that are programmed or configured to execute the deterministic synchronous shaping and machining method based on two-dimensional surface height error by a processor.

[0067] In addition, this embodiment also provides a computer program product, including a computer program / instruction, which is programmed or configured to execute the deterministic synchronous shaping and machining method based on two-dimensional surface height error by a processor.

[0068] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0069] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A deterministic synchronous shaping and machining method based on two-dimensional surface height error, characterized in that, include: S101, Obtain the height error matrix of the optical element to be processed. and height removal function matrix ; S102, the height error matrix Convert to meridian slope error matrix and the slope error matrix of the arc direction The height removal function matrix Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix Substitute the following formula into the residence time calculation model for the multidimensional error of the optical element to be processed: ， In the above formula, The weight value representing the height error. The weighted value representing the slope error along the meridian direction. This represents the weighting value for the slope error in the sagittal direction. Represents the residence time matrix; S103, The residence time matrix is ​​calculated based on the residence time calculation model of multidimensional error. , residence time matrix Arranged according to the two-dimensional surface shape of optical elements to form a two-dimensional residence time And utilize two-dimensional dwell time Deterministic correction of multidimensional errors in optical components to be processed.

2. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 1, characterized in that, In step S102, the height error matrix is... Convert to meridian slope error matrix and the slope error matrix of the arc direction This refers to the height error matrix The meridian slope error matrix is ​​obtained by performing difference operations at adjacent error points in the X and Y directions respectively. and the slope error matrix of the arc direction .

3. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 2, characterized in that, In step S102, the height removal function matrix is... Convert to meridian slope removal function matrix and the slope of the arc direction removal function matrix This refers to removing the height function matrix. The meridian slope removal function matrix is ​​obtained by performing difference operations on adjacent data points in the X and Y directions respectively. and the slope of the arc direction removal function matrix .

4. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 1, characterized in that, Before step S102, a residence time calculation model for the multidimensional error of the optical element to be processed is also established: S201, construct the convolution relationship equation between surface error, dwell time, and removal function as shown in the following equation: ， In the above formula, The two-dimensional height surface shape of the optical element to be processed. For height removal function, This represents the convolution operation. Indicates the two-dimensional dwell time; S202, convert the convolution relationship equation into a system of linear equations: ， In the above formula, Represents the height error matrix. This indicates the removal of the function matrix. Represents the residence time matrix; S203, Based on the aforementioned linear equations, establish a deterministic linear model for shaping and machining of the meridional slope error and the sagittal slope error: ， ， In the above formula, This is the slope error matrix along the meridian direction. The slope error matrix is ​​the arc direction. The function matrix is ​​removed to represent the slope in the meridional direction. Remove the function matrix from the slope of the arc direction; S204 combines the linear equation system, the meridional slope error, and the sagittal slope error of the deterministic shaping linear model to obtain the dwell time solution model for the multidimensional error of the optical element to be processed.

5. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 1, characterized in that, In step S103, the residence time solution model based on multidimensional error calculates the residence time matrix. This refers to a residence time calculation model based on multidimensional error, which uses the LSQR algorithm to calculate the residence time matrix. .

6. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 1, characterized in that, Before step S102, the method further includes obtaining the weight values ​​of the height error configured by the user. Weighting value of meridian slope error and the weighting value of the slope error in the sagittal direction .

7. The deterministic synchronous shaping and machining method based on two-dimensional surface height error according to claim 1, characterized in that, In step S103, the two-dimensional dwell time is utilized. After performing deterministic shaping of the multidimensional errors of the optical element to be processed, the process also includes measuring the height error RMS, meridional slope error RMS, and sagittal slope error RMS of the processed optical element.

8. A deterministic synchronous shaping and machining system based on two-dimensional surface height error, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the deterministic synchronous shaping and machining method based on two-dimensional surface height error as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program / instructions, characterized in that, The computer program / instructions are programmed or configured to execute, via a processor, the deterministic synchronous shaping and machining method based on two-dimensional surface height error as described in any one of claims 1 to 7.

10. A computer program product comprising a computer program / instructions, characterized in that, The computer program / instructions are programmed or configured to execute, via a processor, the deterministic synchronous shaping and machining method based on two-dimensional surface height error as described in any one of claims 1 to 7.

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